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A generalization of the löwdin orthogonalization
Author(s) -
Kashiwagi Hiroshi,
Sasaki Fukashi
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560070758
Subject(s) - orthogonalization , orthonormality , orthonormal basis , matrix (chemical analysis) , generalization , set (abstract data type) , transformation (genetics) , hilbert space , transformation matrix , function (biology) , mathematics , combinatorics , orthogonality , space (punctuation) , mathematical analysis , physics , algorithm , chemistry , quantum mechanics , computer science , geometry , biochemistry , kinematics , gene , programming language , operating system , chromatography , evolutionary biology , biology
The Löwdin orthonormalized set consists of those unique orthonormal functions which minimize the quantity Σ i ∫|g i — f i | 2 dv , i.e., the sum of the squared distances in the Hilbert space between each initial function f f and a corresponding function g g of the orthonormal set. In this paper, the Löwdin orthogonalization is extended to a more general transformation. The new transformation also minimizes the sum Σ i ∫|g i — f i | 2 dv dv , but the overlap matrix of the resultant functions g g is an arbitrary positive definite matrix in contrast to the unit matrix in the Löwdin orthogonalization. The new orbital set may be useful as a basis set for some many‐electron problems in which the smallness of the sum Σ i ∫|g i — f i | 2 dv and a particular form of the overlap matrix are requested at the same time.